Doctor of Philosophy, The Ohio State University, 2006, Philosophy

The central question of this dissertation is whether we are justified in believing in the existence of abstract mathematical objects. In Part I, I provide an in-depth examination and criticism of the most popular argument for the justifiability of believing in the existence of mathematical objects, the Quine-Putnam Indispensability Argument. I argue that the naturalistic basis for the argument not only depends essentially upon an untenable form of radical confirmational holism, but is ultimately self-undermining. In Part II, I examine the most popular argument for the unjustifiability of believing in the existence of abstract mathematical objects, Field's Inexplicability Argument. I argue that not only does the argument ignore contemporary epistemological theories of justified belief and knowledge, but that the justificatory constraint that it suggests is implausible and open to general counterexample. Thus, in Parts I and II, I show that the most popular arguments for and against the justifiability of believing in the existence of abstract mathematical objects rest upon untenable epistemological theories. In Part III, I develop a new epistemological approach to justified belief, validationism. I argue that a validationist constraint on justified belief provides the minimal internalist condition that is needed for being justified and having knowledge. According to validationism, being justified requires one to have “validated” the reliability of the source of one's belief through regular comparison of the output of that source with the output of other established sources. Not only does this approach allow us account for our most fundamental epistemic intuitions, but it helps to explain why justified true beliefs are so valuable. In the end, I apply the validationist approach to the case of mathematics and argue that belief in the existence of abstract mathematical objects cannot be justified.

Committee: Stewart Shapiro (Advisor) Subjects: Philosophy